English

Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets

Classical Analysis and ODEs 2021-02-23 v3 Analysis of PDEs

Abstract

A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond Lipschitz regular domains. Previous results were limited to regular geometric configurations or Hilbertian Sobolev spaces. Sets with porous boundary and their characteristic multipliers on smoothness spaces play a major role in the arguments.

Keywords

Cite

@article{arxiv.1807.02293,
  title  = {Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets},
  author = {Sebastian Bechtel and Moritz Egert},
  journal= {arXiv preprint arXiv:1807.02293},
  year   = {2021}
}

Comments

Upload of the published version including the correction of some further typos

R2 v1 2026-06-23T02:52:39.630Z